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Simplifying 320 = (4x + 5)(x) Reorder the terms: 320 = (5 + 4x)(x) Reorder the terms for easier multiplication: 320 = x(5 + 4x) 320 = (5 * x + 4x * x) 320 = (5x + 4x2) Solving 320 = 5x + 4x2 Solving for variable 'x'. Reorder the terms: 320 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 320 + -5x + -4x2 = 0 + 4x2 + -4x2 320 + -5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 320 + -5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -80 + 1.25x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 1.25x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 1.25x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 1.25x + x2 = 0 + 80 1.25x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 1.25x + x2 = 80 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 80 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 80 + 0.390625 Combine like terms: 80 + 0.390625 = 80.390625 0.390625 + 1.25x + x2 = 80.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 80.390625 Calculate the square root of the right side: 8.96608192 Break this problem into two subproblems by setting (x + 0.625) equal to 8.96608192 and -8.96608192.Subproblem 1
x + 0.625 = 8.96608192 Simplifying x + 0.625 = 8.96608192 Reorder the terms: 0.625 + x = 8.96608192 Solving 0.625 + x = 8.96608192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 8.96608192 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 8.96608192 + -0.625 x = 8.96608192 + -0.625 Combine like terms: 8.96608192 + -0.625 = 8.34108192 x = 8.34108192 Simplifying x = 8.34108192Subproblem 2
x + 0.625 = -8.96608192 Simplifying x + 0.625 = -8.96608192 Reorder the terms: 0.625 + x = -8.96608192 Solving 0.625 + x = -8.96608192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -8.96608192 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -8.96608192 + -0.625 x = -8.96608192 + -0.625 Combine like terms: -8.96608192 + -0.625 = -9.59108192 x = -9.59108192 Simplifying x = -9.59108192Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.34108192, -9.59108192}
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